When a conduit containing moving fluid media is flexurally vibrated in a primary mode having a nonuniform amplitude by an electromagnetic vibrator or other means exerting a lateral vibratory force on the conduit, the dynamic interaction between the primary flexural vibration and the convective motion of the fluid media moving through the conduit generates a secondary flexural vibration. The type of mass flowmeter known as the inertia force flowmeter or Coriolis force flowmeter measures the normalized level of the secondary flexural vibration (ratio of the level or amplitude of the secondary flexural vibration to the level or amplitude of the primary flexural vibration), and determines the mass flow rate of the fluid media moving through the conduit as a function of the measured normalized level of the secondary flexural vibration of the conduit, which normalized level of the secondary flexural vibration is most often measured in the form of a phase angle difference between the flexural vibrations of the two opposite halves of the conduit, or in the form of an electrical variable representing or related to the phase angle difference When the primary flexural vibration of the conduit is generated in a symmetric mode about a midsection of the conduit, the secondary flexural vibration occurs in an antisymmetric mode about the midsection of the conduit. If the primary flexural vibration of the conduit is antisymmetric about the midsection of the conduit, the secondary flexural vibration of the conduit occurs in a symmetric mode about the midsection of the conduit. With an exception for the inertia force flowmeters employing a small caliber vibrating conduit, e.g., less than 0.25 inch or 1 centimeter diameter, the primary flexural vibration of the conduit must be generated by exerting a vibratory force in an action-reaction relationship between two conduits or between two opposite halves of the conduit in order to prevent the supporting structure holding the vibrating conduit or conduits from experiencing mechanical noise vibrations occurring as a reaction to the flexural vibration of the conduit or conduits, which mechanical noise vibrations are highly detrimental in measuring the normalized level of the secondary flexural vibration of the conduit or conduits as a measure of the mass flow rate of media moving through the conduit or conduits.
The two biggest short-comings of the existing versions of the inertia force or Coriolis force mass flowmeters are the extremely high cost of the flowmeters and the very high pressure loss by the fluid media moving through the mass flowmeter. The problem of excessive pressure loss has been addressed by using a pair of vibrating conduits having a straight geometry flexurally vibrated relative to one another instead of a pair of curved or looped conduits having a matched geometry. Unfortunately, the sensitivity (ability to measure low mass flow rates) of the inertia force flowmeter employing a single or a pair of straight conduits is significantly inferior to the sensitivity of the inertia force flowmeter employing a single or a pair of well designed curved or looped conduits. The unreasonably high price of the inertia force flowmeters can be reduced by at least 50 percent by using a single vibrating conduits with two opposite halves thereof flexurally vibrated relative to one another instead of a pair of matched conduit vibrated relative to one another. The problem of exorbitantly high price as well as the problem of excessively high pressure loss existing with the present state of the art in the inertia force flowmeter technology can be successfully addressed by constructing an inertia force flowmeter employing a single looped conduit with a total loop angle equal to 360 degrees, wherein the two opposite halves of the single looped conduit are flexurally vibrated relative to one another in an action-reaction relationship. Cox et al (U.S. Pat. No. 4,127,028), Dahlin et al (U.S. Pat. No. 4,660,421) and Lew (U.S. Pat. No. 4,938,075) disclose a single vibrating looped conduit having a loop angle greater than 540 degrees and less than 720 degrees, wherein the two opposite halves of the looped conduit are flexurally vibrated relative to one another. Levien (U.S. Pat. No. 4,730,501) and Lew (U.S. Pat. No. 4,829,832) disclose the inertia force flowmeters employing a 360 degree loop with two opposite halves flexbrally vibrated relative to one another. Levien's apparatus fails to take the advantage provided by a looped conduit over a straight conduit, as the single looped conduit in Levien's apparatus functions in the exactly same manner as a pair of straight conduits. With the exception of Levien's apparatus that is functionally the same as an inertia force flowmeter employing a pair of straight conduits vibrated relative to one another, all of the above-mentioned prior arts employing a single looped conduit with two opposite halves flexurally vibrated relative to one another in an action-reaction relationship generate the primary flexural vibration in an antisymmetric mode about the center section of the looped conduit and, consequently, the secondary flexural vibration occurs in a symmetric mode about the center section of the looped conduit. In general, the mechanical noise vibrations transmitted to the looped conduit from the ambient structures supporting the looped conduit produce a noise flexural vibration of the looped conduit in a symmetric mode about the center section of the conduit, which symmetric noise flexural vibration cannot be distinguished and separated from the symmetric secondary flexural vibration and, consequently, the mass flow rate of media determined from the measured normalized level of the symmetric component of the resultant flexural vibration of the conduit (sum of the antisymmetric primary flexural vibration and the symmetric secondary and noise flexural vibrations) has a large error introduced by the symmetric noise flexural vibration of the conduit. Lew (U.S. Pat. No. 5,078,014) discloses a solution addressing the problem of the symmetric noise vibration, which solution teaches restraining a midsection of the single looped conduit from experiencing lateral movements. Such a measure drastically reduces the level of the symmetric noise flexural vibration entrained in the resultant flexural vibration of the conduit and, consequently, an inertia force flowmeter employing a single looped conduit with two opposite halves flexurally vibrated relative to one another and a midsection thereof restrained from experiencing lateral movements, provides mass flow measurements with a high degree of accuracy and reliability matching the standard set by the mass flowmeters employing a pair of conduits flexurally vibrated relative to one another. Of course, the pair of conduits flexurally vibrated relative to one another by an electromagnetic vibrator disposed at the center section thereof has the symmetric primary flexural vibration and the antisymmetric secondary flexural vibration, wherein the symmetric noise flexural vibration becomes excluded from the measured normalized level of the antisymmetric component of the resultant flexural vibration of the conduit in the process of determining the mass flow rate of media from the normalized level of the measured antisymmetric component of the resultant flexural vibration of the pair of conduits.